The following table contains numbers of connected regular graphs having girth at least six and with the given degree and number of vertices.
Not necessarily connected 2-regular with girth exactly 6 are given by A026799.
| A014374 | A058348 | |
| Vertices | Degree 3 | Degree 4 |
|---|---|---|
| 14 | 1 | 0 |
| 15 | 0 | 0 |
| 16 | 1 | 0 |
| 17 | 0 | 0 |
| 18 | 5 | 0 |
| 19 | 0 | 0 |
| 20 | 32 | 0 |
| 21 | 0 | 0 |
| 22 | 385 | 0 |
| 23 | 0 | 0 |
| 24 | 7574 | 0 |
| 25 | 0 | 0 |
| 26 | 181227 | 1 |
| 27 | 0 | 0 |
| 28 | 4624501 | 1 |
| 29 | 0 | 0 |
| 30 | 122090544 | 4 |
| 31 | 0 | 0 |
| 32 | 3328929954 | 19 |
| 33 | 0 | 0 |
| 34 | 93990692595 | 1272 |
| 35 | 0 | 25 |
| 36 | 494031 |